### Magnetic Effects Of Current Question 6

#### Question 6 - 2024 (27 Jan Shift 2)

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R _1=2 \pi m$ and $R _2=4 \pi m$ carrying current $I=4 A$ as per figure given below is $\alpha \times 10^{-7} T$. The value of $\alpha$ is (Centre

$O$ is common for all segments)

## Show Answer

#### Answer: (3)

#### Solution:

$\frac{\mu _0 i}{2 R _2}\left(\frac{\pi}{2 \pi}\right) \otimes+\frac{\mu _0 i}{2 R _1}\left(\frac{\pi}{2 \pi}\right) \otimes$

$\left(\frac{\mu _0 i}{4 R _2}+\frac{\mu _0 i}{4 R _1}\right) \otimes$

$\frac{4 \pi \times 10^{-7} \times 4}{4 \times 4 \pi}+\frac{4 \pi \times 10^{-7} \times 4}{4 \times 2 \pi}$

$=3 \times 10^{-7}=\alpha \times 10^{-7}$

$\alpha=3$